Question

If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:

• A. \( -\frac{b^4}{a} \)
• B. \( \frac{b^5}{a} \)
• C. \( -\frac{b^5}{a^2 y^3} \)
• D. \( \frac{b^5}{a^2} \)

Hint:

When differentiating expressions involving constants and variables, remember to apply the chain rule and simplify the resulting expression accordingly.

Answer 1

The Correct Option is C

Given the equation \( y = \frac{b}{a} \), we need to determine \( \frac{dy}{dx} \). The process involves applying the chain rule for differentiation.
- The derivative \( \frac{dy}{dx} \) is contingent upon the relationship between \( y \) and \( x \). In this specific scenario, \( y \) comprises constants \( a \) and \( b \).
- Differentiating \( y = \frac{b}{a} \) using standard differentiation rules yields \( \frac{dy}{dx} \), which simplifies to \( -\frac{b^5}{a^2 y^3} \).
Therefore, the correct answer is option (3).